Geertsma's model for porosity/transit-time relationship

Input(s)

$\mathrm{K}_{\mathrm{b}}$: Bulk Modulus Constant for Formation (dimensionless)

$\sigma_{\mathrm{b}}$: Bulk Density $\left(\mathrm{kg} / \mathrm{m}^{3}\right)$

$\mu_{\mathrm{b}}$: Poisson Ratio for Formation (dimensionless)

$\mathrm{K}_{\mathrm{ma}}$: Bulk Modulus Constant for Matrix (dimensionless)

$\sigma_{\text {ma }}$: Matrix Density $\left(\mathrm{kg} / \mathrm{m}^{3}\right)$

$\mu_{\mathrm{ma}}$: Poisson (dimensionless)

Output(s)

$\mathrm{V}_{\mathrm{b}}$: Acoustic Velocity in Bulk Formation $(\mathrm{m} / \mathrm{s})$

$\mathrm{V}_{\mathrm{ma}}$: Acoustic Velocity in Matrix (m/s)

Formula(s)

$$ \begin{gathered} \mathrm{V}_{\mathrm{b}}=\left(\left(3 * \frac{\mathrm{K}_{\mathrm{b}}}{\sigma_{\mathrm{b}}}\right) *\left(\frac{1-\mu_{\mathrm{b}}}{1+\mu_{\mathrm{b}}}\right)\right)^{0.5} \\ \mathrm{~V}_{\mathrm{ma}}=\left(\left(3 * \frac{\mathrm{K}_{\mathrm{ma}}}{\sigma_{\mathrm{ma}}}\right) *\left(\frac{1-\mu_{\mathrm{ma}}}{1+\mu_{\mathrm{ma}}}\right)\right)^{0.5} \end{gathered} $$

Reference(s)

Bassiouni, Z., 1994, Theory, Measurement, and Interpretation of Well Logs. SPE Textbook Series Vol. 4. Chapter 3, Page: 55.